{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "# Realization of Non-Recursive Filters\n",
    "\n",
    "*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantization Effects\n",
    "\n",
    "Numbers and numerical operations are represented with a finite numerical resolution in digital processors. The same holds for the amplitude values of signals and the algorithmic operations applied to them. Hence, the intended characteristics of a digital filter may deviate in practice due to the finite numerical resolution. The [double-precision floating point representation](https://en.wikipedia.org/wiki/Double-precision_floating-point_format) used in numerical environments like MATLAB or Python/numpy is assumed to be quasi-continuous. This representation serves therefore as reference for the evaluation of quantization effects.\n",
    "\n",
    "This section investigates the consequences of quantization in non-recursive filters. We first take a look on the quantization of the filter coefficients, followed by the effects caused by a finite numerical resolution of the operations. The realization of non-recursive filters is subject to both effects."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantization of Filter Coefficients\n",
    "\n",
    "The output signal $y[k]$ of a non-recursive filter with a finite impulse response (FIR) $h[k]$ of length $N$ is given as\n",
    "\n",
    "\\begin{equation}\n",
    "y[k] = h[k] * x[k] = \\sum_{\\kappa = 0}^{N-1} h[\\kappa] \\; x[k - \\kappa]\n",
    "\\end{equation}\n",
    "\n",
    "where $x[k]$ denotes the input signal. The quantized impulse response $h_Q[k]$ (quantized filter coefficients) is yielded by quantizing the impulse response $h[k]$\n",
    "\n",
    "\\begin{equation}\n",
    "h_Q[k] = \\mathcal{Q} \\{ h[k] \\} = h[k] + e[k]\n",
    "\\end{equation}\n",
    "\n",
    "where $e[k] = h_Q[k] - h[k]$ denotes the [quantization error](../quantization/introduction.ipynb#Model-of-the-Quantization-Process). Introducing $h_Q[k]$ into above equation and rearranging results in\n",
    "\n",
    "\\begin{equation}\n",
    "y_Q[k] = \\sum_{\\kappa = 0}^{N-1} h[\\kappa] \\; x[k - \\kappa] + \\sum_{\\kappa = 0}^{N-1} e[\\kappa] \\; x[k - \\kappa]\n",
    "\\end{equation}\n",
    "\n",
    "The input signal $x[k]$ is filtered by the quantization noise $e[k]$ and superimposed to the desired output of the filter. The overall transfer function $H_Q(e^{j \\Omega})$ of the filter with quantized filter coefficients is given as\n",
    "\n",
    "\\begin{equation}\n",
    "H_Q(e^{j \\Omega}) = \\sum_{k=0}^{N-1} h[k] \\; e^{-j \\Omega k} + \\sum_{k=0}^{N-1} e[k] \\; e^{-j \\Omega k}  = H(e^{j \\Omega}) + E(e^{j \\Omega})\n",
    "\\end{equation}\n",
    "\n",
    "Hence, the quantization of filter coefficients results in a linear distortion of the desired frequency response. To some extent, this distortion can be incorporated into the design of the filter. However, the magnitude of the quantization error $| E(e^{j \\Omega}) |$ cannot get arbitrarily small for a finite quantization step $Q$. This limits the achievable attenuation of a digital filter with quantized coefficients. It is therefore important to normalize the filter coefficients $h[k]$ before quantization in order to keep the relative power of the quantization noise small."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example - Effect of coefficient quantization in a lowpass filter\n",
    "\n",
    "The coefficients of a digital lowpass filter with a cutoff frequency of $\\Omega_0 = \\frac{\\pi}{2}$ are quantized in the following example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.signal as sig\n",
    "\n",
    "w = 8  # wordlength of quantized coefficients\n",
    "A = 1  # attenuation of filter coefficients\n",
    "N = 256  # number of coefficients for filter\n",
    "Q = 1 / (2 ** (w - 1))  # quantization stepsize\n",
    "\n",
    "\n",
    "def uniform_midtread_quantizer(x, Q):\n",
    "    \"\"\"Uniform mid-tread quantizer with limiter.\"\"\"\n",
    "    # limiter\n",
    "    x = np.copy(x)\n",
    "    idx = np.where(x <= -1)\n",
    "    x[idx] = -1\n",
    "    idx = np.where(x > 1 - Q)\n",
    "    x[idx] = 1 - Q\n",
    "    # linear uniform quantization\n",
    "    xQ = Q * np.floor(x / Q + 1 / 2)\n",
    "\n",
    "    return xQ\n",
    "\n",
    "\n",
    "# design lowpass\n",
    "h = A * sig.firwin(N, 0.5)\n",
    "# quantize coefficients\n",
    "hQ = uniform_midtread_quantizer(h, Q)\n",
    "\n",
    "# plot frequency response\n",
    "Om, H = sig.freqz(h)\n",
    "Om, HQ = sig.freqz(hQ)\n",
    "Om, E = sig.freqz(hQ - h)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(Om, 20 * np.log10(np.abs(H)), label=r\"$| H(e^{j \\Omega}) |$ in dB (Designed)\")\n",
    "plt.plot(\n",
    "    Om,\n",
    "    20 * np.log10(np.abs(HQ)),\n",
    "    label=r\"$| H_Q(e^{j \\Omega}) |$ in dB (Quantized coefficients)\",\n",
    ")\n",
    "plt.title(\"Magnitude of the transfer function w and w/o quantization of coefficients\")\n",
    "plt.xlabel(r\"$\\Omega$\")\n",
    "plt.axis([0, np.pi, -130, 10])\n",
    "plt.legend(loc=3)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Change the wordlength `w` of the quantized filter coefficients. How does the magnitude response $| H_Q(e^{j \\Omega}) |$ of the quantized filter change?\n",
    "* Change the attenuation `A` of the filter coefficients. What changes?\n",
    "* Why does the magnitude response of the quantized filter $| H_Q(e^{j \\Omega}) |$ deviate more from the magnitude response of the designed filter $| H(e^{j \\Omega}) |$ in the frequency ranges with high attenuation?\n",
    "\n",
    "Solution: The magnitude response of the quantized filter deviates more from the designed filter the shorter the wordlength `w` is chosen. This is due to the increasing quantization error for shorter wordlengths. The quantization error increases also in comparison to the filter coefficients if their amplitude (attenuation `A`) is small. The deviations from the designed filter are generally higher for high attenuations since the quantization error is additive $H_Q(e^{j \\Omega}) = H(e^{j \\Omega}) + E(e^{j \\Omega})$, as derived above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantization of Signals and Operations\n",
    "\n",
    "Besides the quantization of filter coefficients $h[k]$, also the quantization of the signals, state variables and operations has to be considered in a practical implementation of filters. The computation of the output signal $y[k] = h[k] * x[k]$ of a non-recursive filter by convolution involves multiplications and additions. In digital signal processors numbers are often represented in [fixed-point arithmetic](https://en.wikipedia.org/wiki/Fixed-point_arithmetic) using [two's complement](https://en.wikipedia.org/wiki/Two's_complement). When multiplying two numbers with a wordlength of $w$-bits in this representation the result would require $2w$-bits. Hence the result has to be requantized to $w$-bits. The rounding operation in the quantizer is often realized as truncation of the $w$ least significant bits. The resulting quantization error is known as [round-off error](https://en.wikipedia.org/wiki/Round-off_error). The addition of two numbers may fall outside the maximum/minimum values of the representation and may suffer from clipping. Similar considerations hold also for other number representations, like e.g. [floating point](https://en.wikipedia.org/wiki/Floating_point).\n",
    "\n",
    "As for the [quantization noise](../quantization/linear_uniform_quantization_error.ipynb#Model-for-the-Quantization-Error), a statistical model for the round-off error in multipliers is used to quantify the average impact of round-off noise in a non-recursive filter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model for round-off errors in multipliers\n",
    "\n",
    "As outlined above, multipliers require a requantization of the result in order to keep the wordlength constant. The multiplication of a quantized signal $x_Q[k]$ with a quantized factor $a_Q$ can be written as\n",
    "\n",
    "\\begin{equation}\n",
    "y_Q[k] = \\mathcal{Q} \\{ a_Q \\cdot x_Q[k] \\} = a_Q \\cdot x_Q[k] + e[k]\n",
    "\\end{equation}\n",
    "\n",
    "where the round-off error $e[k]$ is defined as\n",
    "\n",
    "\\begin{equation}\n",
    "e[k] = y_Q[k] - a_Q \\cdot x_Q[k]\n",
    "\\end{equation}\n",
    "\n",
    "This leads to the following model of a multiplier including round-off effects\n",
    "\n",
    "![Model for round-off noise in a multiplier](roundoff_model.png)\n",
    "\n",
    "The round-off error can be modeled statistically in the same way as quantization noise [[Zölzer](../index.ipynb#Literature)]. Under the assumption that the average magnitude of $a_Q \\cdot x_Q[k]$ is much larger that the quantization step size $Q$, the round-off error $e[k]$ can be approximated by the following statistical model\n",
    "\n",
    "1. The round-off error $e[k]$ is not correlated with the input signal $x_Q[k]$\n",
    "\n",
    "2. The round-off error is [white](../random_signals/white_noise.ipynb)\n",
    "\n",
    "    $$ \\Phi_{ee}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\sigma_e^2 $$\n",
    "\n",
    "2. The probability density function (PDF) of the round-off error is given by the zero-mean [uniform distribution](../random_signals/important_distributions.ipynb#Uniform-Distribution)\n",
    "\n",
    "    $$ p_e(\\theta) = \\frac{1}{Q} \\cdot \\text{rect} \\left( \\frac{\\theta}{Q} \\right) $$\n",
    "\n",
    "The variance (power) of the round-off error is [derived from its PDF](../random_signals/important_distributions.ipynb#Uniform-Distribution) as\n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma_e^2 = \\frac{Q^2}{12}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Round-off noise\n",
    "\n",
    "Using above model of a multiplier and discarding clipping, a straightforward realization of the convolution with quantized signals would be to requantize after every multiplication \n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "y_Q[k] &= \\sum_{\\kappa = 0}^{N-1} \\mathcal{Q} \\{ h_Q[\\kappa] \\; x_Q[k - \\kappa] \\} \\\\\n",
    "&= \\sum_{\\kappa = 0}^{N-1} h_Q[\\kappa] \\; x_Q[k - \\kappa] + e[\\kappa] \\\\ \n",
    "&= \\left( \\sum_{\\kappa = 0}^{N-1} h_Q[\\kappa] \\; x_Q[k - \\kappa] \\right) + e_\\text{tot}[k]\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "where $e_\\text{tot}[k] = \\sum_{\\kappa = 0}^{N-1} e[\\kappa]$. The round-off errors $e[\\kappa]$ for each multiplication are uncorrelated to each other. The overall power of the round-off error is then given as\n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma_{e, \\text{tot}}^2 = N \\cdot \\frac{Q^2}{12}\n",
    "\\end{equation}\n",
    "\n",
    "Many digital signal processors allow to perform the multiplications and additions in an internal register with double wordlength. In this case, only the result of the convolution sum has to be requantized \n",
    "\n",
    "\\begin{equation}\n",
    "y_Q[k] = \\mathcal{Q} \\left\\{ \\sum_{\\kappa = 0}^{N-1}  h_Q[\\kappa] \\; x_Q[k - \\kappa] \\right\\} = \n",
    "\\left( \\sum_{\\kappa = 0}^{N-1} h_Q[\\kappa] \\; x_Q[k - \\kappa] \\right) + e[k]\n",
    "\\end{equation}\n",
    "\n",
    "and the total power of the round-off noise in this case is\n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma_{e, \\text{tot}}^2 = \\frac{Q^2}{12}\n",
    "\\end{equation}\n",
    "\n",
    "It is evident that this realization is favorable due to the lower round-off noise, especially for filters with a large number $N$ of coefficients."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example - Effect of requantization after each multiplication\n",
    "\n",
    "The following example simulates the round-off noise of a non-recursive filter when requantization is performed after each multiplication. Clipping is not considered. The input signal $x[k]$ is drawn from a [uniform distribution](../random_signals/important_distributions.ipynb#Uniform-Distribution) with $a=-1$ and $b=1-Q$. Both the input signal and filter coefficients are quantized. The output signal $y[k]$ without requantization of the multiplications is computed, as well as the output signal $y_Q[k]$ with requantization. The statistical properties of the round-off noise $e[k] = y_Q[k] - y[k]$ are evaluated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Power of overall round-off noise is -86.150580 dB\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w = 16  # wordlength of quantized coefficients/operations\n",
    "N = 32  # number of coefficients for filter\n",
    "L = 8192  # length of input signal\n",
    "Q = 1 / (2 ** (w - 1))  # quantization stepsize\n",
    "\n",
    "\n",
    "def uniform_midtread_quantizer(x, Q):\n",
    "    \"\"\"Uniform mid-tread quantizer.\"\"\"\n",
    "    xQ = Q * np.floor(x / Q + 1 / 2)\n",
    "\n",
    "    return xQ\n",
    "\n",
    "\n",
    "# random impulse response\n",
    "h = np.random.uniform(size=N, low=-1, high=1)\n",
    "hQ = uniform_midtread_quantizer(h, Q)\n",
    "# input signal\n",
    "x = np.random.uniform(size=L, low=-1, high=1 - Q)\n",
    "xQ = uniform_midtread_quantizer(x, Q)\n",
    "# output signal by convolution\n",
    "y = np.zeros(L + N - 1)\n",
    "yQ = np.zeros(L + N - 1)\n",
    "for k in np.arange(L):\n",
    "    for kappa in np.arange(N):\n",
    "        if (k - kappa) >= 0:\n",
    "            y[k] += hQ[kappa] * xQ[k - kappa]\n",
    "            yQ[k] += uniform_midtread_quantizer(hQ[kappa] * xQ[k - kappa], Q)\n",
    "\n",
    "# overall round-off error\n",
    "e = yQ - y\n",
    "\n",
    "# estimate power of round-off error\n",
    "sx = 10 * np.log10(np.var(e))\n",
    "print(\"Power of overall round-off noise is %f dB\" % sx)\n",
    "# estimated PDF of round-off error\n",
    "pe, bins = np.histogram(e, bins=50, density=True, range=(-10 * Q, 10 * Q))\n",
    "# estimate PSD of round-off error\n",
    "nf, Pee = sig.welch(e, nperseg=128)\n",
    "\n",
    "\n",
    "# plot statistical properties of error signal\n",
    "plt.figure(figsize=(10, 6))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.bar(bins[:-1] / Q, pe * Q, width=20 / len(pe))\n",
    "plt.title(\"Estimated PDF of the round-off noise\")\n",
    "plt.xlabel(r\"$\\theta / Q$\")\n",
    "plt.ylabel(r\"$\\hat{p}_{e,tot}(\\theta) / Q$\")\n",
    "# plt.axis([-1, 1, 0, 1.2])\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(nf * 2 * np.pi, Pee * 6 / Q**2)\n",
    "plt.title(\"Estimated PSD of the round-off noise\")\n",
    "plt.xlabel(r\"$\\Omega$\")\n",
    "plt.ylabel(r\"$\\hat{\\Phi}_{ee,tot}(e^{j \\Omega}) / \\sigma_e^2$\")\n",
    "plt.axis([0, np.pi, 0, 1.5*N ])\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Change the wordlength `w` and check if the $\\sigma_{e,tot}^2$ derived by numerical simulation is equal to its theoretic value derived above?\n",
    "* Can you explain the shape of the estimated PDF for the round-off noise?\n",
    "\n",
    "Solution: The power of the overall round-off noise was derived above as $\\sigma_{e,tot}^2 = N \\frac{Q}{12}$. Using results from the [model of quantization noise for a uniform quantizer](../quantization/linear_uniform_quantization_error.ipynb#Model-for-the-Quantization-Error) this can be rewritten as $10 \\log_{10} (\\sigma_{e,tot}^2) \\approx 10 \\log_{10} (N) - 10 \\log_{10} (3) - 6.02 w$. Hence a doubling of the filter length results in approximately 3 dB more round-off noise at the filter output. The requantization noise of the individual multiplications can be modeled as uniformly distributed white noise. It follows from the [central limit theorem](https://en.wikipedia.org/wiki/Central_limit_theorem) that the superposition of these individual round-off errors results in a normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example - Comparison of round-off noise of conventional and fast convolution\n",
    "\n",
    "The overall round-off noise in an FIR filter scales with the number of multiplications when rounding is performed after each of these. The fast convolution algorithm requires less multiplications and as a consequence also less rounding operations resulting in potentially less round-off noise at the filter output. This effect is illustrated by the following example. The conventional convolution and the fast convolution is computed for two rectangular signals of the same length $y[k] = A\\cdot\\text{rect}_L[k] * A\\cdot\\text{rect}_L[k]$. The round-off noise is computed by comparing the results to the theoretical result $A^2 L \\cdot \\Lambda_{2L -1}[k]$. Since we cannot change the representation of numbers nor the rounding operations in the given implementation of the FFT, a floating point representation of the signal amplitudes is used for this example. The amplitude $A$ has been chosen such to trigger rounding operations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = 1024  # length of signals x[k]\n",
    "A = 1 / 7  # amplitude of signal\n",
    "M = 2 * L - 1\n",
    "\n",
    "\n",
    "# generate signals\n",
    "x = A * np.ones(L)\n",
    "y = A**2 * L * sig.windows.triang(M)\n",
    "\n",
    "# linear convolution\n",
    "y1 = np.convolve(x, x, \"full\")\n",
    "e1 = y - y1\n",
    "# fast convolution\n",
    "y2 = np.fft.irfft(np.fft.rfft(x, M + 1) * np.fft.rfft(x, M + 1))[0:M]\n",
    "e2 = y - y2\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(np.abs(e1), label=\"conventional convolution\")\n",
    "plt.plot(np.abs(e2), label=\"fast convolution\")\n",
    "plt.xlabel(r\"$k$\")\n",
    "plt.ylabel(r\"$|e[k]|$\")\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercises**\n",
    "\n",
    "* Change the length `L` of the signal. How does the round-off noise scale with length? Why?\n",
    "* Extend above code to compute the power of the round-off noise for various lengths.\n",
    "\n",
    "Solution: The round-off noise scales with the number of multiplications which itself scales by the length `L` of the signal. To some extend this also explains the shape of the round-off errors for the conventional convolution. The two rectangular functions overlap fully in the center which results in the maximum number of non-zero multiplications."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "**Copyright**\n",
    "\n",
    "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples*."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
